Dale Computer Company accepts orders from customers for computers online through

Question

Dale Computer Company accepts orders from customers for computers online through its website and configures and builds them to order at one of its distribution centers from components it orders from its various suppliers in the United States and overseas. It is continually retaining new suppliers as its computer models change and as new computing technologies are developed. It promises its customers that when an order is placed the customer will receive it quickly, typically within a week, which in turn requires that Dale’s suppliers provide component parts as quickly as they are demanded. Normally Dale sets a target of 3 days for a supplier to deliver parts once they are ordered, and Dale uses SPC charts to monitor a supplier’s delivery performance once this target value has been achieved. Dale has learned from past experiences working with many suppliers that it takes some time for new suppliers to improve their production and delivery processes to consistently meet Dale’s target delivery time. It normally takes a supplier about 15 days to deliver Dale’s first order. Determine approximately how many orders it will take a new supplier that has a 70% learning curve to be able to meet Dale’s orders within the specified target time.

Explanation / Answer

The learning curve model states that the time required to produce any items/goods progressively decreases as experience and learning grows. This model is assumed to be exponetial modeled by equation:

Time(n) = Time(1)*Y^f

Time(n) = Time taken to produce nth unit

Time(1) = Time taken to produce first unit

Y = Unit number

f = learning factor determined as ln(% curve)/ln(2)

ln = Natural logarithm

In this case with 70% learning curve

f = ln(0.7) /ln (2) = -0.51457

Time(1) = 15 days in this case – time to produce first unit

Time(n) = 15*(Y)^(-0.51457)

We need to solve for Y such that Time(n) = 3 days which is Dale's target for suppliers.

3 = 15*(Y)^(-0.51457)

3/15 = (Y)^(-0.51457)

0.2 = (Y)^(-0.51457)

Taking natural log on either side

ln(0.2) = -0.51457 * ln(Y)

-1.60943 = -0.51457 * ln(Y)

ln (Y) = 3.1277

Y = exp(3.1277) = 22.82 ~23

So in nutshell it will approximately take 23 orders for the supplier to achieve Dale's target time of 3 days.

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